% Mizar ND problem: t2_asympt_1,asympt_1,324,38 
fof(dh_c1_4__asympt_1,definition,
    ( ( ( v1_asympt_0(c1_4__asympt_1)
        & m1_subset_1(c1_4__asympt_1,k1_numbers) )
     => ! [A] : 
          ( ( v1_asympt_0(A)
            & m1_subset_1(A,k1_numbers) )
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
                      & ~ r1_xreal_0(A,1)
                      & k2_seq_1(k5_numbers,k1_numbers,B,0) = 0
                      & ! [D] : 
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(D,0)
                           => k2_seq_1(k5_numbers,k1_numbers,B,D) = k6_power(c1_4__asympt_1,D) ) )
                      & k2_seq_1(k5_numbers,k1_numbers,C,0) = 0
                      & ! [D] : 
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(D,0)
                           => k2_seq_1(k5_numbers,k1_numbers,C,D) = k6_power(A,D) ) )
                      & ! [D] : 
                          ( ( v1_funct_1(D)
                            & v1_funct_2(D,k5_numbers,k1_numbers)
                            & v4_asympt_0(D)
                            & m2_relset_1(D,k5_numbers,k1_numbers) )
                         => ! [E] : 
                              ( ( v1_funct_1(E)
                                & v1_funct_2(E,k5_numbers,k1_numbers)
                                & v4_asympt_0(E)
                                & m2_relset_1(E,k5_numbers,k1_numbers) )
                             => ~ ( D = B
                                  & E = C
                                  & k5_asympt_0(D) = k5_asympt_0(E) ) ) ) ) ) ) ) )
   => ! [F] : 
        ( ( v1_asympt_0(F)
          & m1_subset_1(F,k1_numbers) )
       => ! [G] : 
            ( ( v1_asympt_0(G)
              & m1_subset_1(G,k1_numbers) )
           => ! [H] : 
                ( ( v1_funct_1(H)
                  & v1_funct_2(H,k5_numbers,k1_numbers)
                  & m2_relset_1(H,k5_numbers,k1_numbers) )
               => ! [I] : 
                    ( ( v1_funct_1(I)
                      & v1_funct_2(I,k5_numbers,k1_numbers)
                      & m2_relset_1(I,k5_numbers,k1_numbers) )
                   => ~ ( ~ r1_xreal_0(F,1)
                        & ~ r1_xreal_0(G,1)
                        & k2_seq_1(k5_numbers,k1_numbers,H,0) = 0
                        & ! [J] : 
                            ( m2_subset_1(J,k1_numbers,k5_numbers)
                           => ( ~ r1_xreal_0(J,0)
                             => k2_seq_1(k5_numbers,k1_numbers,H,J) = k6_power(F,J) ) )
                        & k2_seq_1(k5_numbers,k1_numbers,I,0) = 0
                        & ! [J] : 
                            ( m2_subset_1(J,k1_numbers,k5_numbers)
                           => ( ~ r1_xreal_0(J,0)
                             => k2_seq_1(k5_numbers,k1_numbers,I,J) = k6_power(G,J) ) )
                        & ! [J] : 
                            ( ( v1_funct_1(J)
                              & v1_funct_2(J,k5_numbers,k1_numbers)
                              & v4_asympt_0(J)
                              & m2_relset_1(J,k5_numbers,k1_numbers) )
                           => ! [K] : 
                                ( ( v1_funct_1(K)
                                  & v1_funct_2(K,k5_numbers,k1_numbers)
                                  & v4_asympt_0(K)
                                  & m2_relset_1(K,k5_numbers,k1_numbers) )
                               => ~ ( J = H
                                    & K = I
                                    & k5_asympt_0(J) = k5_asympt_0(K) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_4__asympt_1),file(asympt_1,c1_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c1_4__asympt_1)]).

fof(dh_c2_4__asympt_1,definition,
    ( ( ( v1_asympt_0(c2_4__asympt_1)
        & m1_subset_1(c2_4__asympt_1,k1_numbers) )
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,k5_numbers,k1_numbers)
            & m2_relset_1(A,k5_numbers,k1_numbers) )
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
                  & ~ r1_xreal_0(c2_4__asympt_1,1)
                  & k2_seq_1(k5_numbers,k1_numbers,A,0) = 0
                  & ! [C] : 
                      ( m2_subset_1(C,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(C,0)
                       => k2_seq_1(k5_numbers,k1_numbers,A,C) = k6_power(c1_4__asympt_1,C) ) )
                  & k2_seq_1(k5_numbers,k1_numbers,B,0) = 0
                  & ! [C] : 
                      ( m2_subset_1(C,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(C,0)
                       => k2_seq_1(k5_numbers,k1_numbers,B,C) = k6_power(c2_4__asympt_1,C) ) )
                  & ! [C] : 
                      ( ( v1_funct_1(C)
                        & v1_funct_2(C,k5_numbers,k1_numbers)
                        & v4_asympt_0(C)
                        & m2_relset_1(C,k5_numbers,k1_numbers) )
                     => ! [D] : 
                          ( ( v1_funct_1(D)
                            & v1_funct_2(D,k5_numbers,k1_numbers)
                            & v4_asympt_0(D)
                            & m2_relset_1(D,k5_numbers,k1_numbers) )
                         => ~ ( C = A
                              & D = B
                              & k5_asympt_0(C) = k5_asympt_0(D) ) ) ) ) ) ) )
   => ! [E] : 
        ( ( v1_asympt_0(E)
          & m1_subset_1(E,k1_numbers) )
       => ! [F] : 
            ( ( v1_funct_1(F)
              & v1_funct_2(F,k5_numbers,k1_numbers)
              & m2_relset_1(F,k5_numbers,k1_numbers) )
           => ! [G] : 
                ( ( v1_funct_1(G)
                  & v1_funct_2(G,k5_numbers,k1_numbers)
                  & m2_relset_1(G,k5_numbers,k1_numbers) )
               => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
                    & ~ r1_xreal_0(E,1)
                    & k2_seq_1(k5_numbers,k1_numbers,F,0) = 0
                    & ! [H] : 
                        ( m2_subset_1(H,k1_numbers,k5_numbers)
                       => ( ~ r1_xreal_0(H,0)
                         => k2_seq_1(k5_numbers,k1_numbers,F,H) = k6_power(c1_4__asympt_1,H) ) )
                    & k2_seq_1(k5_numbers,k1_numbers,G,0) = 0
                    & ! [H] : 
                        ( m2_subset_1(H,k1_numbers,k5_numbers)
                       => ( ~ r1_xreal_0(H,0)
                         => k2_seq_1(k5_numbers,k1_numbers,G,H) = k6_power(E,H) ) )
                    & ! [H] : 
                        ( ( v1_funct_1(H)
                          & v1_funct_2(H,k5_numbers,k1_numbers)
                          & v4_asympt_0(H)
                          & m2_relset_1(H,k5_numbers,k1_numbers) )
                       => ! [I] : 
                            ( ( v1_funct_1(I)
                              & v1_funct_2(I,k5_numbers,k1_numbers)
                              & v4_asympt_0(I)
                              & m2_relset_1(I,k5_numbers,k1_numbers) )
                           => ~ ( H = F
                                & I = G
                                & k5_asympt_0(H) = k5_asympt_0(I) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_4__asympt_1),file(asympt_1,c2_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c2_4__asympt_1)]).

fof(dh_c3_4__asympt_1,definition,
    ( ( ( v1_funct_1(c3_4__asympt_1)
        & v1_funct_2(c3_4__asympt_1,k5_numbers,k1_numbers)
        & m2_relset_1(c3_4__asympt_1,k5_numbers,k1_numbers) )
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,k5_numbers,k1_numbers)
            & m2_relset_1(A,k5_numbers,k1_numbers) )
         => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
              & ~ r1_xreal_0(c2_4__asympt_1,1)
              & k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,0) = 0
              & ! [B] : 
                  ( m2_subset_1(B,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(B,0)
                   => k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,B) = k6_power(c1_4__asympt_1,B) ) )
              & k2_seq_1(k5_numbers,k1_numbers,A,0) = 0
              & ! [B] : 
                  ( m2_subset_1(B,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(B,0)
                   => k2_seq_1(k5_numbers,k1_numbers,A,B) = k6_power(c2_4__asympt_1,B) ) )
              & ! [B] : 
                  ( ( v1_funct_1(B)
                    & v1_funct_2(B,k5_numbers,k1_numbers)
                    & v4_asympt_0(B)
                    & m2_relset_1(B,k5_numbers,k1_numbers) )
                 => ! [C] : 
                      ( ( v1_funct_1(C)
                        & v1_funct_2(C,k5_numbers,k1_numbers)
                        & v4_asympt_0(C)
                        & m2_relset_1(C,k5_numbers,k1_numbers) )
                     => ~ ( B = c3_4__asympt_1
                          & C = A
                          & k5_asympt_0(B) = k5_asympt_0(C) ) ) ) ) ) )
   => ! [D] : 
        ( ( v1_funct_1(D)
          & v1_funct_2(D,k5_numbers,k1_numbers)
          & m2_relset_1(D,k5_numbers,k1_numbers) )
       => ! [E] : 
            ( ( v1_funct_1(E)
              & v1_funct_2(E,k5_numbers,k1_numbers)
              & m2_relset_1(E,k5_numbers,k1_numbers) )
           => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
                & ~ r1_xreal_0(c2_4__asympt_1,1)
                & k2_seq_1(k5_numbers,k1_numbers,D,0) = 0
                & ! [F] : 
                    ( m2_subset_1(F,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(F,0)
                     => k2_seq_1(k5_numbers,k1_numbers,D,F) = k6_power(c1_4__asympt_1,F) ) )
                & k2_seq_1(k5_numbers,k1_numbers,E,0) = 0
                & ! [F] : 
                    ( m2_subset_1(F,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(F,0)
                     => k2_seq_1(k5_numbers,k1_numbers,E,F) = k6_power(c2_4__asympt_1,F) ) )
                & ! [F] : 
                    ( ( v1_funct_1(F)
                      & v1_funct_2(F,k5_numbers,k1_numbers)
                      & v4_asympt_0(F)
                      & m2_relset_1(F,k5_numbers,k1_numbers) )
                   => ! [G] : 
                        ( ( v1_funct_1(G)
                          & v1_funct_2(G,k5_numbers,k1_numbers)
                          & v4_asympt_0(G)
                          & m2_relset_1(G,k5_numbers,k1_numbers) )
                       => ~ ( F = D
                            & G = E
                            & k5_asympt_0(F) = k5_asympt_0(G) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_4__asympt_1),file(asympt_1,c3_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c3_4__asympt_1)]).

fof(dh_c4_4__asympt_1,definition,
    ( ( ( v1_funct_1(c4_4__asympt_1)
        & v1_funct_2(c4_4__asympt_1,k5_numbers,k1_numbers)
        & m2_relset_1(c4_4__asympt_1,k5_numbers,k1_numbers) )
     => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
          & ~ r1_xreal_0(c2_4__asympt_1,1)
          & k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,0) = 0
          & ! [A] : 
              ( m2_subset_1(A,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(A,0)
               => k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,A) = k6_power(c1_4__asympt_1,A) ) )
          & k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,0) = 0
          & ! [A] : 
              ( m2_subset_1(A,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(A,0)
               => k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,A) = k6_power(c2_4__asympt_1,A) ) )
          & ! [A] : 
              ( ( v1_funct_1(A)
                & v1_funct_2(A,k5_numbers,k1_numbers)
                & v4_asympt_0(A)
                & m2_relset_1(A,k5_numbers,k1_numbers) )
             => ! [B] : 
                  ( ( v1_funct_1(B)
                    & v1_funct_2(B,k5_numbers,k1_numbers)
                    & v4_asympt_0(B)
                    & m2_relset_1(B,k5_numbers,k1_numbers) )
                 => ~ ( A = c3_4__asympt_1
                      & B = c4_4__asympt_1
                      & k5_asympt_0(A) = k5_asympt_0(B) ) ) ) ) )
   => ! [C] : 
        ( ( v1_funct_1(C)
          & v1_funct_2(C,k5_numbers,k1_numbers)
          & m2_relset_1(C,k5_numbers,k1_numbers) )
       => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
            & ~ r1_xreal_0(c2_4__asympt_1,1)
            & k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,0) = 0
            & ! [D] : 
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( ~ r1_xreal_0(D,0)
                 => k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,D) = k6_power(c1_4__asympt_1,D) ) )
            & k2_seq_1(k5_numbers,k1_numbers,C,0) = 0
            & ! [D] : 
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( ~ r1_xreal_0(D,0)
                 => k2_seq_1(k5_numbers,k1_numbers,C,D) = k6_power(c2_4__asympt_1,D) ) )
            & ! [D] : 
                ( ( v1_funct_1(D)
                  & v1_funct_2(D,k5_numbers,k1_numbers)
                  & v4_asympt_0(D)
                  & m2_relset_1(D,k5_numbers,k1_numbers) )
               => ! [E] : 
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,k5_numbers,k1_numbers)
                      & v4_asympt_0(E)
                      & m2_relset_1(E,k5_numbers,k1_numbers) )
                   => ~ ( D = c3_4__asympt_1
                        & E = C
                        & k5_asympt_0(D) = k5_asympt_0(E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_4__asympt_1),file(asympt_1,c4_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c4_4__asympt_1)]).

fof(e1_4__asympt_1,assumption,(
    ~ r1_xreal_0(c1_4__asympt_1,1) ),
    introduced(assumption,[file(asympt_1,e1_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,e1_4__asympt_1)]).

fof(e2_4__asympt_1,assumption,(
    ~ r1_xreal_0(c2_4__asympt_1,1) ),
    introduced(assumption,[file(asympt_1,e2_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,e2_4__asympt_1)]).

fof(e3_4__asympt_1,assumption,
    ( k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,0) = 0
    & ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ~ r1_xreal_0(A,0)
         => k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,A) = k6_power(c1_4__asympt_1,A) ) ) ),
    introduced(assumption,[file(asympt_1,e3_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,e3_4__asympt_1)]).

fof(e4_4__asympt_1,assumption,
    ( k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,0) = 0
    & ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ~ r1_xreal_0(A,0)
         => k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,A) = k6_power(c2_4__asympt_1,A) ) ) ),
    introduced(assumption,[file(asympt_1,e4_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,e4_4__asympt_1)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(rc1_asympt_0,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(asympt_0,rc1_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,rc1_asympt_0)]).

fof(rc2_asympt_0,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(asympt_0,rc2_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,rc2_asympt_0)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(rc5_asympt_0,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A) ) ),
    file(asympt_0,rc5_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,rc5_asympt_0)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc3_asympt_0,theorem,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v2_asympt_0(A)
          & v5_asympt_0(A) )
       => ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v1_seq_1(A)
          & v4_asympt_0(A) ) ) ) ),
    file(asympt_0,cc3_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,cc3_asympt_0)]).

fof(cc3_int_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    [interesting(0.9),axiom,file(int_1,cc3_int_1)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    [interesting(0.9),axiom,file(int_1,cc4_int_1)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(rc1_int_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    [interesting(0.9),axiom,file(int_1,rc1_int_1)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(rc2_int_1,theorem,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    [interesting(0.9),axiom,file(int_1,rc2_int_1)]).

fof(rc4_asympt_0,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(asympt_0,rc4_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,rc4_asympt_0)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(cc2_asympt_0,theorem,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v4_asympt_0(A) )
       => ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v1_seq_1(A)
          & v2_asympt_0(A)
          & v5_asympt_0(A) ) ) ) ),
    file(asympt_0,cc2_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,cc2_asympt_0)]).

fof(cc2_int_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    [interesting(0.9),axiom,file(int_1,cc2_int_1)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k5_asympt_0,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_fraenkel(k5_asympt_0(A),k5_numbers,k1_numbers) ) ),
    file(asympt_0,k5_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,k5_asympt_0)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_c3_4__asympt_1,assumption,
    ( v1_funct_1(c3_4__asympt_1)
    & v1_funct_2(c3_4__asympt_1,k5_numbers,k1_numbers)
    & m2_relset_1(c3_4__asympt_1,k5_numbers,k1_numbers) ),
    introduced(assumption,[file(asympt_1,c3_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c3_4__asympt_1)]).

fof(dt_c4_4__asympt_1,assumption,
    ( v1_funct_1(c4_4__asympt_1)
    & v1_funct_2(c4_4__asympt_1,k5_numbers,k1_numbers)
    & m2_relset_1(c4_4__asympt_1,k5_numbers,k1_numbers) ),
    introduced(assumption,[file(asympt_1,c4_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c4_4__asympt_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(de_c5_4__asympt_1,definition,(
    c5_4__asympt_1 = c3_4__asympt_1 ),
    introduced(definition,[new_symbol(c5_4__asympt_1),file(asympt_1,c5_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c5_4__asympt_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k5_power,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => v1_xreal_0(k5_power(A,B)) ) ),
    file(power,k5_power),
    [interesting(0.9),axiom,file(power,k5_power)]).

fof(rc3_asympt_0,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_asympt_0(A) ) ),
    file(asympt_0,rc3_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,rc3_asympt_0)]).

fof(rc6_asympt_0,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v1_asympt_0(A) ) ),
    file(asympt_0,rc6_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,rc6_asympt_0)]).

fof(t1_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

fof(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

fof(t4_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    [interesting(0.9),axiom,file(real,t4_real)]).

fof(t5_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

fof(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k2_seq_1,definition,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(seq_1,k2_seq_1),
    [interesting(0.9),axiom,file(seq_1,k2_seq_1)]).

fof(redefinition_k6_power,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k6_power(A,B) = k5_power(A,B) ) ),
    file(power,k6_power),
    [interesting(0.9),axiom,file(power,k6_power)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ),
    file(seq_1,k2_seq_1),
    [interesting(0.9),axiom,file(seq_1,k2_seq_1)]).

fof(dt_k6_power,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k6_power(A,B),k1_numbers) ) ),
    file(power,k6_power),
    [interesting(0.9),axiom,file(power,k6_power)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_c1_4__asympt_1,assumption,
    ( v1_asympt_0(c1_4__asympt_1)
    & m1_subset_1(c1_4__asympt_1,k1_numbers) ),
    introduced(assumption,[file(asympt_1,c1_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c1_4__asympt_1)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,(
    r1_xreal_0(0,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,(
    r1_xreal_0(1,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

fof(l3_asympt_1,plain,(
    ! [A] : 
      ( ( v1_asympt_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( k2_seq_1(k5_numbers,k1_numbers,B,0) = 0
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k6_power(A,C) ) ) )
           => ( r1_xreal_0(A,1)
              | v4_asympt_0(B) ) ) ) ) ),
    file(asympt_1,l3_asympt_1),
    [interesting(0.9),axiom,file(asympt_1,l3_asympt_1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,(
    ~ r1_xreal_0(1,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]).

fof(e5_4__asympt_1,plain,
    ( v1_funct_1(c3_4__asympt_1)
    & v1_funct_2(c3_4__asympt_1,k5_numbers,k1_numbers)
    & v4_asympt_0(c3_4__asympt_1)
    & m2_relset_1(c3_4__asympt_1,k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_asympt_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rc6_asympt_0,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k5_numbers,dt_k6_power,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,cc2_int_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,t1_numerals,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_4__asympt_1,e3_4__asympt_1,l3_asympt_1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.8),file(asympt_1,e5_4__asympt_1),[file(asympt_1,e5_4__asympt_1)]]).

fof(dt_c5_4__asympt_1,plain,
    ( v1_funct_1(c5_4__asympt_1)
    & v1_funct_2(c5_4__asympt_1,k5_numbers,k1_numbers)
    & v4_asympt_0(c5_4__asympt_1)
    & m2_relset_1(c5_4__asympt_1,k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_asympt_0,rc2_asympt_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_asympt_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc6_membered,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_int_1,rc4_asympt_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc2_asympt_0,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_relset_1,dt_c3_4__asympt_1,fc2_membered,de_c5_4__asympt_1,e5_4__asympt_1]),
    [interesting(0.8),file(asympt_1,c5_4__asympt_1),[file(asympt_1,c5_4__asympt_1)]]).

fof(de_c6_4__asympt_1,definition,(
    c6_4__asympt_1 = c4_4__asympt_1 ),
    introduced(definition,[new_symbol(c6_4__asympt_1),file(asympt_1,c6_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c6_4__asympt_1)]).

fof(dt_c2_4__asympt_1,assumption,
    ( v1_asympt_0(c2_4__asympt_1)
    & m1_subset_1(c2_4__asympt_1,k1_numbers) ),
    introduced(assumption,[file(asympt_1,c2_4__asympt_1)]),
    [interesting(0.8),axiom,file(asympt_1,c2_4__asympt_1)]).

fof(e6_4__asympt_1,plain,
    ( v1_funct_1(c4_4__asympt_1)
    & v1_funct_2(c4_4__asympt_1,k5_numbers,k1_numbers)
    & v4_asympt_0(c4_4__asympt_1)
    & m2_relset_1(c4_4__asympt_1,k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_asympt_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rc6_asympt_0,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k5_numbers,dt_k6_power,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,cc2_int_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,t1_numerals,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_4__asympt_1,e4_4__asympt_1,l3_asympt_1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.8),file(asympt_1,e6_4__asympt_1),[file(asympt_1,e6_4__asympt_1)]]).

fof(dt_c6_4__asympt_1,plain,
    ( v1_funct_1(c6_4__asympt_1)
    & v1_funct_2(c6_4__asympt_1,k5_numbers,k1_numbers)
    & v4_asympt_0(c6_4__asympt_1)
    & m2_relset_1(c6_4__asympt_1,k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_asympt_0,rc2_asympt_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_asympt_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc6_membered,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_int_1,rc4_asympt_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc2_asympt_0,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_relset_1,dt_c4_4__asympt_1,fc2_membered,de_c6_4__asympt_1,e6_4__asympt_1]),
    [interesting(0.8),file(asympt_1,c6_4__asympt_1),[file(asympt_1,c6_4__asympt_1)]]).

fof(commutativity_k3_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    [interesting(0.9),axiom,file(funct_2,k1_funct_2)]).

fof(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]).

fof(fc21_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc21_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc21_xreal_0)]).

fof(fc22_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc22_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc22_xreal_0)]).

fof(fc23_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc23_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc23_xreal_0)]).

fof(fc24_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc24_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc24_xreal_0)]).

fof(fc2_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_int_1(k3_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc2_int_1),
    [interesting(0.9),axiom,file(int_1,fc2_int_1)]).

fof(fc4_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc4_xreal_0)]).

fof(fc7_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & v1_int_1(k3_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc7_int_1),
    [interesting(0.9),axiom,file(int_1,fc7_int_1)]).

fof(rqRealMult__k3_xcmplx_0__r0_r0_r0,theorem,(
    k3_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)]).

fof(spc7_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_arithm)]).

fof(t2_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,0) = 0 ) ),
    file(arithm,t2_arithm),
    [interesting(0.9),axiom,file(arithm,t2_arithm)]).

fof(commutativity_k4_real_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k4_real_1(B,A) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(redefinition_k1_fraenkel,definition,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]).

fof(redefinition_k4_real_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(redefinition_m2_fraenkel,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]).

fof(dt_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]).

fof(fraenkel_a_1_0_asympt_0,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v2_asympt_0(B)
        & m2_relset_1(B,k5_numbers,k1_numbers) )
     => ( r2_hidden(A,a_1_0_asympt_0(B))
      <=> ? [C] : 
            ( m2_fraenkel(C,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers))
            & A = C
            & ? [D] : 
                ( m1_subset_1(D,k1_numbers)
                & ? [E] : 
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                    & ~ r1_xreal_0(D,0)
                    & ! [F] : 
                        ( m2_subset_1(F,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(E,F)
                         => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,F),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,B,F)))
                            & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,C,F)) ) ) ) ) ) ) ) ) ),
    file(asympt_0,a_1_0_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,a_1_0_asympt_0)]).

fof(d12_asympt_0,definition,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => k5_asympt_0(A) = a_1_0_asympt_0(A) ) ),
    file(asympt_0,d12_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,d12_asympt_0)]).

fof(dh_c1_4_1__asympt_1,definition,
    ( ( ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1))
       => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1)) )
      & ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1))
       => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1)) ) )
   => ! [A] : 
        ( ( r2_hidden(A,k5_asympt_0(c5_4__asympt_1))
         => r2_hidden(A,k5_asympt_0(c6_4__asympt_1)) )
        & ( r2_hidden(A,k5_asympt_0(c6_4__asympt_1))
         => r2_hidden(A,k5_asympt_0(c5_4__asympt_1)) ) ) ),
    introduced(definition,[new_symbol(c1_4_1__asympt_1),file(asympt_1,c1_4_1__asympt_1)]),
    [interesting(0.65),axiom,file(asympt_1,c1_4_1__asympt_1)]).

fof(e1_4_1_1__asympt_1,assumption,(
    r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1)) ),
    introduced(assumption,[file(asympt_1,e1_4_1_1__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,e1_4_1_1__asympt_1)]).

fof(t3_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(1,A) = A ) ),
    file(arithm,t3_arithm),
    [interesting(0.9),axiom,file(arithm,t3_arithm)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(dt_c1_4_1__asympt_1,assumption,(
    $true ),
    introduced(assumption,[file(asympt_1,c1_4_1__asympt_1)]),
    [interesting(0.65),axiom,file(asympt_1,c1_4_1__asympt_1)]).

fof(dh_c1_4_1_1__asympt_1,definition,
    ( ? [A] : 
        ( m2_fraenkel(A,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers))
        & c1_4_1__asympt_1 = A
        & ? [B] : 
            ( m1_subset_1(B,k1_numbers)
            & ? [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ~ r1_xreal_0(B,0)
                & ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(C,D)
                     => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,D),k4_real_1(B,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,D)))
                        & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,A,D)) ) ) ) ) ) )
   => ( m2_fraenkel(c1_4_1_1__asympt_1,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers))
      & c1_4_1__asympt_1 = c1_4_1_1__asympt_1
      & ? [E] : 
          ( m1_subset_1(E,k1_numbers)
          & ? [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
              & ~ r1_xreal_0(E,0)
              & ! [G] : 
                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(F,G)
                   => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,G),k4_real_1(E,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,G)))
                      & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,G)) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_4_1_1__asympt_1),file(asympt_1,c1_4_1_1__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,c1_4_1_1__asympt_1)]).

fof(e2_4_1_1__asympt_1,plain,(
    ? [A] : 
      ( m2_fraenkel(A,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers))
      & c1_4_1__asympt_1 = A
      & ? [B] : 
          ( m1_subset_1(B,k1_numbers)
          & ? [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & ~ r1_xreal_0(B,0)
              & ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,D),k4_real_1(B,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,D)))
                      & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,A,D)) ) ) ) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,fc6_membered,rc1_membered,commutativity_k3_xcmplx_0,existence_m1_fraenkel,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,dt_c3_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc7_arithm,t1_real,t2_arithm,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,t2_tarski,fraenkel_a_1_0_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_subset_1,redefinition_k1_fraenkel,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_fraenkel,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_asympt_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_subset_1,dt_c1_4_1__asympt_1,dt_c5_4__asympt_1,de_c5_4__asympt_1,cc2_int_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,t1_numerals,t1_subset,t7_boole,d12_asympt_0,spc0_numerals,spc0_boole,e1_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e2_4_1_1__asympt_1),[file(asympt_1,e2_4_1_1__asympt_1)]]).

fof(dt_c1_4_1_1__asympt_1,plain,(
    m2_fraenkel(c1_4_1_1__asympt_1,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers)) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_fraenkel,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_fraenkel,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_subset_1,dt_c1_4_1__asympt_1,dt_c5_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c1_4_1_1__asympt_1,e2_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,c1_4_1_1__asympt_1),[file(asympt_1,c1_4_1_1__asympt_1)]]).

fof(dh_c2_4_1_1__asympt_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & ~ r1_xreal_0(A,0)
            & ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(B,C)
                 => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C),k4_real_1(A,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,C)))
                    & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C)) ) ) ) ) )
   => ( m1_subset_1(c2_4_1_1__asympt_1,k1_numbers)
      & ? [D] : 
          ( m2_subset_1(D,k1_numbers,k5_numbers)
          & ~ r1_xreal_0(c2_4_1_1__asympt_1,0)
          & ! [E] : 
              ( m2_subset_1(E,k1_numbers,k5_numbers)
             => ( r1_xreal_0(D,E)
               => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,E),k4_real_1(c2_4_1_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,E)))
                  & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,E)) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_4_1_1__asympt_1),file(asympt_1,c2_4_1_1__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,c2_4_1_1__asympt_1)]).

fof(e4_4_1_1__asympt_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & ~ r1_xreal_0(A,0)
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C),k4_real_1(A,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,C)))
                  & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C)) ) ) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_fraenkel,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_fraenkel,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_subset_1,dt_c1_4_1__asympt_1,dt_c1_4_1_1__asympt_1,dt_c5_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c1_4_1_1__asympt_1,e2_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e4_4_1_1__asympt_1),[file(asympt_1,e4_4_1_1__asympt_1)]]).

fof(e5_4_1_1__asympt_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & ~ r1_xreal_0(A,0)
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C),k4_real_1(A,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,C)))
                  & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C)) ) ) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,commutativity_k3_xcmplx_0,existence_m1_relset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c3_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc7_arithm,t1_real,t2_arithm,t2_real,t2_subset,t3_real,t3_subset,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_4_1_1__asympt_1,dt_c5_4__asympt_1,de_c5_4__asympt_1,cc2_int_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,t1_numerals,spc0_numerals,spc0_boole,e4_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e5_4_1_1__asympt_1),[file(asympt_1,e5_4_1_1__asympt_1)]]).

fof(dt_c2_4_1_1__asympt_1,plain,(
    m1_subset_1(c2_4_1_1__asympt_1,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_4_1_1__asympt_1,dt_c5_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c2_4_1_1__asympt_1,e5_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,c2_4_1_1__asympt_1),[file(asympt_1,c2_4_1_1__asympt_1)]]).

fof(rqRealMult__k3_xcmplx_0__r0_r1_r0,theorem,(
    k3_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)]).

fof(rqRealMult__k3_xcmplx_0__r1_r0_r0,theorem,(
    k3_xcmplx_0(1,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0)]).

fof(fc10_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]).

fof(fc11_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]).

fof(fc12_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]).

fof(fc1_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_int_1(k2_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc1_int_1),
    [interesting(0.9),axiom,file(int_1,fc1_int_1)]).

fof(fc3_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]).

fof(fc6_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_int_1(k2_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc6_int_1),
    [interesting(0.9),axiom,file(int_1,fc6_int_1)]).

fof(fc7_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]).

fof(fc8_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]).

fof(fc9_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]).

fof(spc6_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_arithm)]).

fof(commutativity_k2_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(commutativity_k1_nat_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(redefinition_k1_nat_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(dh_c3_4_1_1__asympt_1,definition,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & ~ r1_xreal_0(c2_4_1_1__asympt_1,0)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r1_xreal_0(A,B)
             => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,B),k4_real_1(c2_4_1_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,B)))
                & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,B)) ) ) ) )
   => ( m2_subset_1(c3_4_1_1__asympt_1,k1_numbers,k5_numbers)
      & ~ r1_xreal_0(c2_4_1_1__asympt_1,0)
      & ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ( r1_xreal_0(c3_4_1_1__asympt_1,C)
           => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C),k4_real_1(c2_4_1_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,C)))
              & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,C)) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_4_1_1__asympt_1),file(asympt_1,c3_4_1_1__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,c3_4_1_1__asympt_1)]).

fof(dt_c3_4_1_1__asympt_1,plain,(
    m2_subset_1(c3_4_1_1__asympt_1,k1_numbers,k5_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_4_1_1__asympt_1,dt_c2_4_1_1__asympt_1,dt_c5_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c2_4_1_1__asympt_1,dh_c3_4_1_1__asympt_1,e5_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,c3_4_1_1__asympt_1),[file(asympt_1,c3_4_1_1__asympt_1)]]).

fof(de_c1_4_1_1_1__asympt_1,definition,(
    c1_4_1_1_1__asympt_1 = k1_nat_1(c3_4_1_1__asympt_1,1) ),
    introduced(definition,[new_symbol(c1_4_1_1_1__asympt_1),file(asympt_1,c1_4_1_1_1__asympt_1)]),
    [interesting(0.35),axiom,file(asympt_1,c1_4_1_1_1__asympt_1)]).

fof(dt_c1_4_1_1_1__asympt_1,plain,(
    m2_subset_1(c1_4_1_1_1__asympt_1,k1_numbers,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c3_4_1_1__asympt_1,fc2_membered,spc1_numerals,spc1_boole,de_c1_4_1_1_1__asympt_1]),
    [interesting(0.35),file(asympt_1,c1_4_1_1_1__asympt_1),[file(asympt_1,c1_4_1_1_1__asympt_1)]]).

fof(dh_c2_4_1_1_1__asympt_1,definition,
    ( ( m2_subset_1(c2_4_1_1_1__asympt_1,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c1_4_1_1_1__asympt_1,c2_4_1_1_1__asympt_1)
       => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_1_1__asympt_1)))
          & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r1_xreal_0(c1_4_1_1_1__asympt_1,A)
         => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,A),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,A)))
            & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,A)) ) ) ) ),
    introduced(definition,[new_symbol(c2_4_1_1_1__asympt_1),file(asympt_1,c2_4_1_1_1__asympt_1)]),
    [interesting(0.35),axiom,file(asympt_1,c2_4_1_1_1__asympt_1)]).

fof(e1_4_1_1_1__asympt_1,assumption,(
    r1_xreal_0(c1_4_1_1_1__asympt_1,c2_4_1_1_1__asympt_1) ),
    introduced(assumption,[file(asympt_1,e1_4_1_1_1__asympt_1)]),
    [interesting(0.35),axiom,file(asympt_1,e1_4_1_1_1__asympt_1)]).

fof(fc14_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc14_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc14_xreal_0)]).

fof(fc15_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc15_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc15_xreal_0)]).

fof(fc16_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc16_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc16_xreal_0)]).

fof(fc19_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v2_xreal_0(k6_xcmplx_0(A,B))
        & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc19_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc19_xreal_0)]).

fof(fc20_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v2_xreal_0(k6_xcmplx_0(B,A))
        & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc20_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc20_xreal_0)]).

fof(fc3_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc3_int_1),
    [interesting(0.9),axiom,file(int_1,fc3_int_1)]).

fof(fc4_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_int_1(k6_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc4_int_1),
    [interesting(0.9),axiom,file(int_1,fc4_int_1)]).

fof(fc8_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v1_int_1(k6_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc8_int_1),
    [interesting(0.9),axiom,file(int_1,fc8_int_1)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,(
    k2_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,(
    k2_xcmplx_0(0,1) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,theorem,(
    k2_xcmplx_0(0,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,(
    k2_xcmplx_0(1,0) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,theorem,(
    k2_xcmplx_0(1,k4_xcmplx_0(1)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),1) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]).

fof(spc1_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) ),
    file(arithm,spc1_arithm),
    [interesting(0.9),axiom,file(arithm,spc1_arithm)]).

fof(spc5_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ),
    file(arithm,spc5_arithm),
    [interesting(0.9),axiom,file(arithm,spc5_arithm)]).

fof(spc8_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) ),
    file(arithm,spc8_arithm),
    [interesting(0.9),axiom,file(arithm,spc8_arithm)]).

fof(t1_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    [interesting(0.9),axiom,file(arithm,t1_arithm)]).

fof(fc13_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc13_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc13_xreal_0)]).

fof(fc17_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v2_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc17_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc17_xreal_0)]).

fof(fc18_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A))
        & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc18_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc18_xreal_0)]).

fof(fc1_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc1_xreal_0)]).

fof(fc5_int_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc5_int_1),
    [interesting(0.9),axiom,file(int_1,fc5_int_1)]).

fof(fc5_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc5_xreal_0)]).

fof(fc9_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_int_1(k6_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc9_int_1),
    [interesting(0.9),axiom,file(int_1,fc9_int_1)]).

fof(spc2_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,k4_xcmplx_0(1)) = k4_xcmplx_0(A) ) ),
    file(arithm,spc2_arithm),
    [interesting(0.9),axiom,file(arithm,spc2_arithm)]).

fof(spc9_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ),
    file(arithm,spc9_arithm),
    [interesting(0.9),axiom,file(arithm,spc9_arithm)]).

fof(t4_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    [interesting(0.9),axiom,file(arithm,t4_arithm)]).

fof(involutiveness_k4_xcmplx_0,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]).

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]).

fof(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]).

fof(dt_c2_4_1_1_1__asympt_1,assumption,(
    m2_subset_1(c2_4_1_1_1__asympt_1,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(asympt_1,c2_4_1_1_1__asympt_1)]),
    [interesting(0.35),axiom,file(asympt_1,c2_4_1_1_1__asympt_1)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rm1,theorem,(
    ~ r1_xreal_0(0,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rm1,theorem,(
    ~ r1_xreal_0(1,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_r0,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_r1,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rm1,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,(
    k6_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,(
    k6_xcmplx_0(1,0) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]).

fof(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]).

fof(rqRealNeg__k4_xcmplx_0__r0_r0,theorem,(
    k4_xcmplx_0(0) = 0 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)]).

fof(rqRealNeg__k4_xcmplx_0__r1_rm1,theorem,(
    k4_xcmplx_0(1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,(
    k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0,theorem,(
    k6_xcmplx_0(1,1) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)]).

fof(e1_4_1_1_1_1__asympt_1,plain,(
    k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_1_1__asympt_1) = k6_power(c1_4__asympt_1,c2_4_1_1_1__asympt_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,e1_4_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1_1__asympt_1])],[commutativity_k2_xcmplx_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc20_xreal_0,fc3_int_1,fc3_xreal_0,fc4_int_1,fc4_subset_1,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,t1_arithm,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k1_nat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k1_nat_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c3_4_1_1__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc5_int_1,fc5_membered,fc5_xreal_0,fc9_int_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc9_arithm,t1_numerals,t1_real,t2_subset,t3_subset,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_power,dt_k6_xcmplx_0,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c1_4_1_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c3_4__asympt_1,dt_c5_4__asympt_1,de_c1_4_1_1_1__asympt_1,de_c5_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_4__asympt_1,e1_4_1_1_1__asympt_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.2),file(asympt_1,e1_4_1_1_1_1__asympt_1),[file(asympt_1,e1_4_1_1_1_1__asympt_1)]]).

fof(d3_asympt_0,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_asympt_0(A)
      <=> ( ~ r1_xreal_0(A,0)
          & A != 1 ) ) ) ),
    file(asympt_0,d3_asympt_0),
    [interesting(0.9),axiom,file(asympt_0,d3_asympt_0)]).

fof(e7_4__asympt_1,plain,
    ( ~ r1_xreal_0(c1_4__asympt_1,0)
    & c1_4__asympt_1 != 1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c1_4__asympt_1,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d3_asympt_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(asympt_1,e7_4__asympt_1),[file(asympt_1,e7_4__asympt_1)]]).

fof(e8_4__asympt_1,plain,
    ( ~ r1_xreal_0(c2_4__asympt_1,0)
    & c2_4__asympt_1 != 1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c2_4__asympt_1,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d3_asympt_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(asympt_1,e8_4__asympt_1),[file(asympt_1,e8_4__asympt_1)]]).

fof(t64_power,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(A,0)
                  & A != 1
                  & ~ r1_xreal_0(B,0)
                  & B != 1
                  & ~ r1_xreal_0(C,0)
                  & k5_power(A,C) != k3_xcmplx_0(k5_power(A,B),k5_power(B,C)) ) ) ) ) ),
    file(power,t64_power),
    [interesting(0.9),axiom,file(power,t64_power)]).

fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,(
    k3_xcmplx_0(1,1) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]).

fof(e2_4_1_1_1_1__asympt_1,plain,(
    k6_power(c1_4__asympt_1,c2_4_1_1_1__asympt_1) = k4_real_1(k6_power(c1_4__asympt_1,c2_4__asympt_1),k6_power(c2_4__asympt_1,c2_4_1_1_1__asympt_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c1_4__asympt_1,dt_c2_4__asympt_1,e1_4_1_1_1__asympt_1])],[reflexivity_r1_tarski,commutativity_k2_xcmplx_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc3_int_1,fc3_xreal_0,fc4_int_1,fc5_membered,fc6_int_1,fc6_membered,fc7_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc5_arithm,spc6_arithm,spc8_arithm,t1_arithm,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k1_nat_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c3_4_1_1__asympt_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc23_xreal_0,fc2_membered,fc5_int_1,fc9_int_1,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc2_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_real_1,redefinition_k6_power,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_power,dt_k6_power,dt_k6_xcmplx_0,dt_c1_4__asympt_1,dt_c1_4_1_1_1__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_1_1__asympt_1,de_c1_4_1_1_1__asympt_1,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e7_4__asympt_1,e8_4__asympt_1,e1_4_1_1_1__asympt_1,t64_power,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.2),file(asympt_1,e2_4_1_1_1_1__asympt_1),[file(asympt_1,e2_4_1_1_1_1__asympt_1)]]).

fof(e5_4_1_1_1__asympt_1,plain,(
    k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_1_1__asympt_1) = k4_real_1(k6_power(c1_4__asympt_1,c2_4__asympt_1),k6_power(c2_4__asympt_1,c2_4_1_1_1__asympt_1)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c1_4__asympt_1,dt_c2_4__asympt_1,e1_4_1_1_1__asympt_1])],[e1_4_1_1_1_1__asympt_1,e2_4_1_1_1_1__asympt_1]),
    [interesting(0.35),file(asympt_1,e5_4_1_1_1__asympt_1),[file(asympt_1,e5_4_1_1_1__asympt_1)]]).

fof(fc27_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc27_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc27_xreal_0)]).

fof(fc28_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(B,A))
        & v1_xreal_0(k7_xcmplx_0(B,A))
        & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc28_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc28_xreal_0)]).

fof(fc29_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc29_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc29_xreal_0)]).

fof(fc30_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc30_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc30_xreal_0)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2,theorem,(
    k2_xcmplx_0(0,2) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,theorem,(
    k2_xcmplx_0(0,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,theorem,(
    k2_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,theorem,(
    k2_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,(
    k2_xcmplx_0(1,1) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,theorem,(
    k2_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2,theorem,(
    k2_xcmplx_0(2,0) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1,theorem,(
    k2_xcmplx_0(2,k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0,theorem,(
    k2_xcmplx_0(2,k4_xcmplx_0(2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),2) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),2) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)]).

fof(t5_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(0,A) = 0 ) ),
    file(arithm,t5_arithm),
    [interesting(0.9),axiom,file(arithm,t5_arithm)]).

fof(t6_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,1) = A ) ),
    file(arithm,t6_arithm),
    [interesting(0.9),axiom,file(arithm,t6_arithm)]).

fof(dt_k7_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k7_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]).

fof(fc6_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc6_xreal_0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r2,theorem,(
    r1_xreal_0(0,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rm2,theorem,(
    ~ r1_xreal_0(0,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn1d2,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rnm1d2,theorem,(
    ~ r1_xreal_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r2,theorem,(
    r1_xreal_0(1,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rm2,theorem,(
    ~ r1_xreal_0(1,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn1d2,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rnm1d2,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r0,theorem,(
    ~ r1_xreal_0(2,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r1,theorem,(
    ~ r1_xreal_0(2,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r2,theorem,(
    r1_xreal_0(2,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rm1,theorem,(
    ~ r1_xreal_0(2,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rm2,theorem,(
    ~ r1_xreal_0(2,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn1d2,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rnm1d2,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_r2,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rm2,theorem,(
    ~ r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rn1d2,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r0,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r1,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r2,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_rm1,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_rm2,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r0,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,theorem,(
    k6_xcmplx_0(0,2) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(2)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,theorem,(
    k6_xcmplx_0(1,2) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,theorem,(
    k6_xcmplx_0(1,k4_xcmplx_0(1)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2,theorem,(
    k6_xcmplx_0(2,0) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1,theorem,(
    k6_xcmplx_0(2,1) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0,theorem,(
    k6_xcmplx_0(2,2) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,(
    k7_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r2_r0,theorem,(
    k7_xcmplx_0(0,2) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,theorem,(
    k7_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,(
    k7_xcmplx_0(1,1) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,theorem,(
    k7_xcmplx_0(1,2) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(1,2)) = 2 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]).

fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2,theorem,(
    k7_xcmplx_0(2,1) = 2 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2)]).

fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1,theorem,(
    k7_xcmplx_0(2,2) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1)]).

fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,(
    k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]).

fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,theorem,(
    k7_xcmplx_0(k4_xcmplx_0(1),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]).

fof(rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,(
    k7_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1)]).

fof(rqRealNeg__k4_xcmplx_0__r2_rm2,theorem,(
    k4_xcmplx_0(2) = k4_xcmplx_0(2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)]).

fof(rqRealNeg__k4_xcmplx_0__rm2_r2,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(2)) = 2 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)]).

fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]).

fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]).

fof(spc2_numerals,theorem,
    ( v2_xreal_0(2)
    & m2_subset_1(2,k1_numbers,k5_numbers)
    & m1_subset_1(2,k5_numbers)
    & m1_subset_1(2,k1_numbers) ),
    file(numerals,spc2_numerals),
    [interesting(0.9),axiom,file(numerals,spc2_numerals)]).

fof(spc2_boole,theorem,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    [interesting(0.9),axiom,file(boole,spc2_boole)]).

fof(t10_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(B,A)
                      & r1_xreal_0(C,D)
                      & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ),
    file(xreal_1,t10_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t10_xreal_1)]).

fof(e2_4_1_1_1__asympt_1,plain,(
    ~ r1_xreal_0(k1_nat_1(c3_4_1_1__asympt_1,1),k1_nat_1(c3_4_1_1__asympt_1,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_int_1,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,rc5_asympt_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc6_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_c3_4_1_1__asympt_1,cc2_xreal_0,fc3_xreal_0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t10_xreal_1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.35),file(asympt_1,e2_4_1_1_1__asympt_1),[file(asympt_1,e2_4_1_1_1__asympt_1)]]).

fof(t2_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t2_xreal_1)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]).

fof(e3_4_1_1_1__asympt_1,plain,(
    ~ r1_xreal_0(c2_4_1_1_1__asympt_1,c3_4_1_1__asympt_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1,e1_4_1_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc3_int_1,fc4_int_1,fc5_membered,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_int_1,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc2_membered,fc30_xreal_0,fc3_xreal_0,fc5_int_1,fc8_xreal_0,fc9_int_1,rc1_xreal_0,rc5_asympt_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealAdd__k2_xcmplx_0__rm1_r2_r1,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_4_1_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c3_4_1_1__asympt_1,de_c1_4_1_1_1__asympt_1,cc2_xreal_0,fc1_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e2_4_1_1_1__asympt_1,e1_4_1_1_1__asympt_1,t2_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.35),file(asympt_1,e3_4_1_1_1__asympt_1),[file(asympt_1,e3_4_1_1_1__asympt_1)]]).

fof(e7_4_1_1__asympt_1,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c3_4_1_1__asympt_1,A)
       => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,A),k4_real_1(c2_4_1_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,A)))
          & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,A)) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_4_1_1__asympt_1,dt_c2_4_1_1__asympt_1,dt_c3_4_1_1__asympt_1,dt_c5_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c2_4_1_1__asympt_1,dh_c3_4_1_1__asympt_1,e5_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e7_4_1_1__asympt_1),[file(asympt_1,e7_4_1_1__asympt_1)]]).

fof(e4_4_1_1_1__asympt_1,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1),k4_real_1(c2_4_1_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_1_1__asympt_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4_1_1_1__asympt_1,e1_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c3_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_asympt_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_4_1_1__asympt_1,dt_c2_4_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c3_4_1_1__asympt_1,dt_c5_4__asympt_1,de_c5_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_4_1_1_1__asympt_1,e7_4_1_1__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(asympt_1,e4_4_1_1_1__asympt_1),[file(asympt_1,e4_4_1_1_1__asympt_1)]]).

fof(e6_4_1_1_1__asympt_1,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k6_power(c2_4__asympt_1,c2_4_1_1_1__asympt_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__asympt_1,dt_c2_4_1_1_1__asympt_1,e1_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc3_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,dt_c3_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc4_xreal_0,fc5_int_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc2_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_power,dt_c1_4__asympt_1,dt_c1_4_1_1__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c5_4__asympt_1,de_c5_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e5_4_1_1_1__asympt_1,e4_4_1_1_1__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.35),file(asympt_1,e6_4_1_1_1__asympt_1),[file(asympt_1,e6_4_1_1_1__asympt_1)]]).

fof(e7_4_1_1_1__asympt_1,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_1_1__asympt_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_4__asympt_1,e2_4__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1,e4_4__asympt_1,e1_4_1_1_1__asympt_1])],[commutativity_k2_xcmplx_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc3_int_1,fc3_xreal_0,fc4_int_1,fc4_subset_1,fc6_int_1,fc6_membered,fc7_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc5_arithm,spc6_arithm,spc8_arithm,t1_arithm,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k1_nat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_k1_nat_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_nat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c3_4_1_1__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc4_xreal_0,fc5_int_1,fc5_membered,fc5_xreal_0,fc9_int_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc2_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_power,dt_k6_xcmplx_0,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c1_4_1_1__asympt_1,dt_c1_4_1_1_1__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c4_4__asympt_1,dt_c6_4__asympt_1,de_c1_4_1_1_1__asympt_1,de_c6_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e6_4_1_1_1__asympt_1,e4_4__asympt_1,e1_4_1_1_1__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.35),file(asympt_1,e7_4_1_1_1__asympt_1),[file(asympt_1,e7_4_1_1_1__asympt_1)]]).

fof(e8_4_1_1_1__asympt_1,plain,(
    r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1,e1_4_1_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,spc7_arithm,t1_subset,t2_arithm,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k3_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c3_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc2_subset_1,rqRealMult__k3_xcmplx_0__r0_r0_r0,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_4_1_1__asympt_1,dt_c2_4_1_1__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c3_4_1_1__asympt_1,dt_c5_4__asympt_1,de_c5_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e7_4_1_1__asympt_1,e3_4_1_1_1__asympt_1]),
    [interesting(0.35),file(asympt_1,e8_4_1_1_1__asympt_1),[file(asympt_1,e8_4_1_1_1__asympt_1)]]).

fof(i5_4_1_1_1__asympt_1,theorem,(
    $true ),
    introduced(tautology,[file(asympt_1,i5_4_1_1_1__asympt_1)]),
    [interesting(0.35),trivial,file(asympt_1,i5_4_1_1_1__asympt_1)]).

fof(i4_4_1_1_1__asympt_1,plain,(
    r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1,e1_4_1_1_1__asympt_1])],[e8_4_1_1_1__asympt_1,i5_4_1_1_1__asympt_1]),
    [interesting(0.35),file(asympt_1,i4_4_1_1_1__asympt_1),[file(asympt_1,i4_4_1_1_1__asympt_1)]]).

fof(i3_4_1_1_1__asympt_1,plain,
    ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_1_1__asympt_1)))
    & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_4__asympt_1,e2_4__asympt_1,dt_c2_4__asympt_1,e4_4__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1,e1_4_1_1_1__asympt_1])],[e7_4_1_1_1__asympt_1,i4_4_1_1_1__asympt_1]),
    [interesting(0.35),file(asympt_1,i3_4_1_1_1__asympt_1),[file(asympt_1,i3_4_1_1_1__asympt_1)]]).

fof(i2_4_1_1_1__asympt_1,plain,
    ( r1_xreal_0(c1_4_1_1_1__asympt_1,c2_4_1_1_1__asympt_1)
   => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_1_1__asympt_1)))
      & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_4__asympt_1,e2_4__asympt_1,dt_c2_4__asympt_1,e4_4__asympt_1,dt_c2_4_1_1_1__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1]),discharge_asm(discharge,[e1_4_1_1_1__asympt_1])],[e1_4_1_1_1__asympt_1,i3_4_1_1_1__asympt_1]),
    [interesting(0.35),file(asympt_1,i2_4_1_1_1__asympt_1),[file(asympt_1,i2_4_1_1_1__asympt_1)]]).

fof(i2_4_1_1_1_tmp__asympt_1,plain,
    ( m2_subset_1(c2_4_1_1_1__asympt_1,k1_numbers,k5_numbers)
   => ( r1_xreal_0(c1_4_1_1_1__asympt_1,c2_4_1_1_1__asympt_1)
     => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_1_1__asympt_1)))
        & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,c2_4_1_1_1__asympt_1)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_4__asympt_1,e2_4__asympt_1,dt_c2_4__asympt_1,e4_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1]),discharge_asm(discharge,[dt_c2_4_1_1_1__asympt_1])],[dt_c2_4_1_1_1__asympt_1,i2_4_1_1_1__asympt_1]),
    [interesting(0.35),i1_4_1_1_1__asympt_1]).

fof(i1_4_1_1_1__asympt_1,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c1_4_1_1_1__asympt_1,A)
       => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,A),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,A)))
          & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,A)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_4__asympt_1,e2_4__asympt_1,dt_c2_4__asympt_1,e4_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[i2_4_1_1_1_tmp__asympt_1,dh_c2_4_1_1_1__asympt_1]),
    [interesting(0.35),file(asympt_1,i1_4_1_1_1__asympt_1),[file(asympt_1,i1_4_1_1_1__asympt_1)]]).

fof(e11_4_1_1__asympt_1,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,B),k4_real_1(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,B)))
              & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c1_4_1_1__asympt_1,B)) ) ) ) ) ),
    inference(take,[status(thm),assumptions([dt_c4_4__asympt_1,e2_4__asympt_1,dt_c2_4__asympt_1,e4_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_asympt_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rc6_asympt_0,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc2_subset_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_k6_power,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c1_4_1_1__asympt_1,dt_c1_4_1_1_1__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_1__asympt_1,dt_c6_4__asympt_1,fc2_membered,spc0_numerals,spc0_boole,i1_4_1_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e11_4_1_1__asympt_1),[file(asympt_1,e11_4_1_1__asympt_1)]]).

fof(e3_4_1_1__asympt_1,plain,(
    c1_4_1__asympt_1 = c1_4_1_1__asympt_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dh_c1_4_1_1__asympt_1,e2_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e3_4_1_1__asympt_1),[file(asympt_1,e3_4_1_1__asympt_1)]]).

fof(t65_power,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(A,1)
                  & ~ r1_xreal_0(B,0)
                  & ~ r1_xreal_0(C,B)
                  & r1_xreal_0(k5_power(A,C),k5_power(A,B)) ) ) ) ) ),
    file(power,t65_power),
    [interesting(0.9),axiom,file(power,t65_power)]).

fof(e8_4_1_1__asympt_1,plain,(
    ~ r1_xreal_0(k6_power(c1_4__asympt_1,c2_4__asympt_1),k6_power(c1_4__asympt_1,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1,dt_c2_4__asympt_1,e1_4__asympt_1,e2_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k6_power,dt_k5_power,dt_k6_power,dt_c1_4__asympt_1,dt_c2_4__asympt_1,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_4__asympt_1,e2_4__asympt_1,t65_power,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.5),file(asympt_1,e8_4_1_1__asympt_1),[file(asympt_1,e8_4_1_1__asympt_1)]]).

fof(t59_power,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(A,0)
          & A != 1
          & k5_power(A,1) != 0 ) ) ),
    file(power,t59_power),
    [interesting(0.9),axiom,file(power,t59_power)]).

fof(e9_4_1_1__asympt_1,plain,(
    ~ r1_xreal_0(k6_power(c1_4__asympt_1,c2_4__asympt_1),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__asympt_1,e1_4__asympt_1,e2_4__asympt_1,dt_c1_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k6_power,dt_k5_power,dt_k6_power,dt_c1_4__asympt_1,dt_c2_4__asympt_1,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e8_4_1_1__asympt_1,e7_4__asympt_1,t59_power,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.5),file(asympt_1,e9_4_1_1__asympt_1),[file(asympt_1,e9_4_1_1__asympt_1)]]).

fof(e6_4_1_1__asympt_1,plain,(
    ~ r1_xreal_0(c2_4_1_1__asympt_1,0) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[dh_c2_4_1_1__asympt_1,dh_c3_4_1_1__asympt_1,e5_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e6_4_1_1__asympt_1),[file(asympt_1,e6_4_1_1__asympt_1)]]).

fof(t70_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(C,B)
                  & r1_xreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(B,A)) ) ) ) ) ),
    file(xreal_1,t70_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t70_xreal_1)]).

fof(e10_4_1_1__asympt_1,plain,(
    ~ r1_xreal_0(k4_real_1(c2_4_1_1__asympt_1,k6_power(c1_4__asympt_1,c2_4__asympt_1)),k4_real_1(c2_4_1_1__asympt_1,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__asympt_1,e2_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc5_membered,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_power,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_real_1,redefinition_k6_power,dt_k3_xcmplx_0,dt_k4_real_1,dt_k6_power,dt_c1_4__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_1__asympt_1,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e9_4_1_1__asympt_1,e6_4_1_1__asympt_1,t70_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(asympt_1,e10_4_1_1__asympt_1),[file(asympt_1,e10_4_1_1__asympt_1)]]).

fof(e12_4_1_1__asympt_1,plain,(
    r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_4__asympt_1,e4_4__asympt_1,dt_c2_4__asympt_1,e2_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[reflexivity_r1_tarski,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c4_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_0_asympt_0,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k5_asympt_0,dt_k5_numbers,dt_k6_power,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4_1_1__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_1__asympt_1,dt_c6_4__asympt_1,de_c6_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,t1_subset,t7_boole,d12_asympt_0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e11_4_1_1__asympt_1,e3_4_1_1__asympt_1,e10_4_1_1__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(asympt_1,e12_4_1_1__asympt_1),[file(asympt_1,e12_4_1_1__asympt_1)]]).

fof(i2_4_1_1__asympt_1,theorem,(
    $true ),
    introduced(tautology,[file(asympt_1,i2_4_1_1__asympt_1)]),
    [interesting(0.5),trivial,file(asympt_1,i2_4_1_1__asympt_1)]).

fof(i1_4_1_1__asympt_1,plain,(
    r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_4__asympt_1,e4_4__asympt_1,dt_c2_4__asympt_1,e2_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1,e1_4_1_1__asympt_1])],[e12_4_1_1__asympt_1,i2_4_1_1__asympt_1]),
    [interesting(0.5),file(asympt_1,i1_4_1_1__asympt_1),[file(asympt_1,i1_4_1_1__asympt_1)]]).

fof(e1_4_1__asympt_1,plain,
    ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1))
   => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_4__asympt_1,e4_4__asympt_1,dt_c2_4__asympt_1,e2_4__asympt_1,dt_c1_4_1__asympt_1,dt_c1_4__asympt_1,dt_c3_4__asympt_1,e1_4__asympt_1,e3_4__asympt_1]),discharge_asm(discharge,[e1_4_1_1__asympt_1])],[e1_4_1_1__asympt_1,i1_4_1_1__asympt_1]),
    [interesting(0.65),file(asympt_1,e1_4_1__asympt_1),[file(asympt_1,e1_4_1__asympt_1)]]).

fof(e2_4_1__asympt_1,assumption,(
    r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1)) ),
    introduced(assumption,[file(asympt_1,e2_4_1__asympt_1)]),
    [interesting(0.65),axiom,file(asympt_1,e2_4_1__asympt_1)]).

fof(dh_c2_4_1__asympt_1,definition,
    ( ? [A] : 
        ( m2_fraenkel(A,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers))
        & c1_4_1__asympt_1 = A
        & ? [B] : 
            ( m1_subset_1(B,k1_numbers)
            & ? [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ~ r1_xreal_0(B,0)
                & ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(C,D)
                     => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,D),k4_real_1(B,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,D)))
                        & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,A,D)) ) ) ) ) ) )
   => ( m2_fraenkel(c2_4_1__asympt_1,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers))
      & c1_4_1__asympt_1 = c2_4_1__asympt_1
      & ? [E] : 
          ( m1_subset_1(E,k1_numbers)
          & ? [F] : 
              ( m2_subset_1(F,k1_numbers,k5_numbers)
              & ~ r1_xreal_0(E,0)
              & ! [G] : 
                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(F,G)
                   => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,G),k4_real_1(E,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,G)))
                      & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,G)) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_4_1__asympt_1),file(asympt_1,c2_4_1__asympt_1)]),
    [interesting(0.65),axiom,file(asympt_1,c2_4_1__asympt_1)]).

fof(e3_4_1__asympt_1,plain,(
    ? [A] : 
      ( m2_fraenkel(A,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers))
      & c1_4_1__asympt_1 = A
      & ? [B] : 
          ( m1_subset_1(B,k1_numbers)
          & ? [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & ~ r1_xreal_0(B,0)
              & ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,D),k4_real_1(B,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,D)))
                      & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,A,D)) ) ) ) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,fc6_membered,rc1_membered,commutativity_k3_xcmplx_0,existence_m1_fraenkel,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,dt_c4_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc7_arithm,t1_real,t2_arithm,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,t2_tarski,fraenkel_a_1_0_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_subset_1,redefinition_k1_fraenkel,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_fraenkel,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_asympt_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_subset_1,dt_c1_4_1__asympt_1,dt_c6_4__asympt_1,de_c6_4__asympt_1,cc2_int_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,t1_numerals,t1_subset,t7_boole,d12_asympt_0,spc0_numerals,spc0_boole,e2_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,e3_4_1__asympt_1),[file(asympt_1,e3_4_1__asympt_1)]]).

fof(dt_c2_4_1__asympt_1,plain,(
    m2_fraenkel(c2_4_1__asympt_1,k5_numbers,k1_numbers,k1_fraenkel(k5_numbers,k1_numbers)) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_fraenkel,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_fraenkel,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_subset_1,dt_c1_4_1__asympt_1,dt_c6_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c2_4_1__asympt_1,e3_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,c2_4_1__asympt_1),[file(asympt_1,c2_4_1__asympt_1)]]).

fof(dh_c3_4_1__asympt_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & ~ r1_xreal_0(A,0)
            & ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(B,C)
                 => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C),k4_real_1(A,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,C)))
                    & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C)) ) ) ) ) )
   => ( m1_subset_1(c3_4_1__asympt_1,k1_numbers)
      & ? [D] : 
          ( m2_subset_1(D,k1_numbers,k5_numbers)
          & ~ r1_xreal_0(c3_4_1__asympt_1,0)
          & ! [E] : 
              ( m2_subset_1(E,k1_numbers,k5_numbers)
             => ( r1_xreal_0(D,E)
               => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,E),k4_real_1(c3_4_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,E)))
                  & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,E)) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_4_1__asympt_1),file(asympt_1,c3_4_1__asympt_1)]),
    [interesting(0.65),axiom,file(asympt_1,c3_4_1__asympt_1)]).

fof(e5_4_1__asympt_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & ~ r1_xreal_0(A,0)
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C),k4_real_1(A,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,C)))
                  & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C)) ) ) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_fraenkel,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_fraenkel,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_subset_1,dt_c1_4_1__asympt_1,dt_c2_4_1__asympt_1,dt_c6_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c2_4_1__asympt_1,e3_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,e5_4_1__asympt_1),[file(asympt_1,e5_4_1__asympt_1)]]).

fof(e6_4_1__asympt_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & ~ r1_xreal_0(A,0)
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C),k4_real_1(A,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,C)))
                  & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C)) ) ) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,commutativity_k3_xcmplx_0,existence_m1_relset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c4_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc7_arithm,t1_real,t2_arithm,t2_real,t2_subset,t3_real,t3_subset,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c2_4_1__asympt_1,dt_c6_4__asympt_1,de_c6_4__asympt_1,cc2_int_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,t1_numerals,spc0_numerals,spc0_boole,e5_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,e6_4_1__asympt_1),[file(asympt_1,e6_4_1__asympt_1)]]).

fof(dt_c3_4_1__asympt_1,plain,(
    m1_subset_1(c3_4_1__asympt_1,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c2_4_1__asympt_1,dt_c6_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c3_4_1__asympt_1,e6_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,c3_4_1__asympt_1),[file(asympt_1,c3_4_1__asympt_1)]]).

fof(dh_c4_4_1__asympt_1,definition,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & ~ r1_xreal_0(c3_4_1__asympt_1,0)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r1_xreal_0(A,B)
             => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,B),k4_real_1(c3_4_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,B)))
                & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,B)) ) ) ) )
   => ( m2_subset_1(c4_4_1__asympt_1,k1_numbers,k5_numbers)
      & ~ r1_xreal_0(c3_4_1__asympt_1,0)
      & ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ( r1_xreal_0(c4_4_1__asympt_1,C)
           => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C),k4_real_1(c3_4_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,C)))
              & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,C)) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_4_1__asympt_1),file(asympt_1,c4_4_1__asympt_1)]),
    [interesting(0.65),axiom,file(asympt_1,c4_4_1__asympt_1)]).

fof(dt_c4_4_1__asympt_1,plain,(
    m2_subset_1(c4_4_1__asympt_1,k1_numbers,k5_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c2_4_1__asympt_1,dt_c3_4_1__asympt_1,dt_c6_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c3_4_1__asympt_1,dh_c4_4_1__asympt_1,e6_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,c4_4_1__asympt_1),[file(asympt_1,c4_4_1__asympt_1)]]).

fof(de_c1_4_1_2__asympt_1,definition,(
    c1_4_1_2__asympt_1 = k1_nat_1(c4_4_1__asympt_1,1) ),
    introduced(definition,[new_symbol(c1_4_1_2__asympt_1),file(asympt_1,c1_4_1_2__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,c1_4_1_2__asympt_1)]).

fof(dt_c1_4_1_2__asympt_1,plain,(
    m2_subset_1(c1_4_1_2__asympt_1,k1_numbers,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c4_4_1__asympt_1,fc2_membered,spc1_numerals,spc1_boole,de_c1_4_1_2__asympt_1]),
    [interesting(0.5),file(asympt_1,c1_4_1_2__asympt_1),[file(asympt_1,c1_4_1_2__asympt_1)]]).

fof(dh_c2_4_1_2__asympt_1,definition,
    ( ( m2_subset_1(c2_4_1_2__asympt_1,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c1_4_1_2__asympt_1,c2_4_1_2__asympt_1)
       => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_2__asympt_1)))
          & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r1_xreal_0(c1_4_1_2__asympt_1,A)
         => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,A),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,A)))
            & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,A)) ) ) ) ),
    introduced(definition,[new_symbol(c2_4_1_2__asympt_1),file(asympt_1,c2_4_1_2__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,c2_4_1_2__asympt_1)]).

fof(e1_4_1_2__asympt_1,assumption,(
    r1_xreal_0(c1_4_1_2__asympt_1,c2_4_1_2__asympt_1) ),
    introduced(assumption,[file(asympt_1,e1_4_1_2__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,e1_4_1_2__asympt_1)]).

fof(dt_c2_4_1_2__asympt_1,assumption,(
    m2_subset_1(c2_4_1_2__asympt_1,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(asympt_1,c2_4_1_2__asympt_1)]),
    [interesting(0.5),axiom,file(asympt_1,c2_4_1_2__asympt_1)]).

fof(e1_4_1_2_1__asympt_1,plain,(
    k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_2__asympt_1) = k6_power(c2_4__asympt_1,c2_4_1_2__asympt_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,e2_4_1__asympt_1,dt_c2_4_1_2__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e1_4_1_2__asympt_1])],[commutativity_k2_xcmplx_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc20_xreal_0,fc3_int_1,fc3_xreal_0,fc4_int_1,fc4_subset_1,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc6_arithm,spc8_arithm,t1_arithm,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k1_nat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k1_nat_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c4_4_1__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc5_int_1,fc5_membered,fc5_xreal_0,fc9_int_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc9_arithm,t1_numerals,t1_real,t2_subset,t3_subset,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_power,dt_k6_xcmplx_0,dt_m2_subset_1,dt_c1_4_1_2__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_2__asympt_1,dt_c4_4__asympt_1,dt_c6_4__asympt_1,de_c1_4_1_2__asympt_1,de_c6_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_4__asympt_1,e1_4_1_2__asympt_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.35),file(asympt_1,e1_4_1_2_1__asympt_1),[file(asympt_1,e1_4_1_2_1__asympt_1)]]).

fof(e2_4_1_2_1__asympt_1,plain,(
    k6_power(c2_4__asympt_1,c2_4_1_2__asympt_1) = k4_real_1(k6_power(c2_4__asympt_1,c1_4__asympt_1),k6_power(c1_4__asympt_1,c2_4_1_2__asympt_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1,dt_c2_4_1_2__asympt_1,dt_c1_4__asympt_1,dt_c2_4__asympt_1,e1_4_1_2__asympt_1])],[reflexivity_r1_tarski,commutativity_k2_xcmplx_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc3_int_1,fc3_xreal_0,fc4_int_1,fc5_membered,fc6_int_1,fc6_membered,fc7_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc5_arithm,spc6_arithm,spc8_arithm,t1_arithm,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k1_nat_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c4_4_1__asympt_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc23_xreal_0,fc2_membered,fc5_int_1,fc9_int_1,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc2_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_real_1,redefinition_k6_power,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_power,dt_k6_power,dt_k6_xcmplx_0,dt_c1_4__asympt_1,dt_c1_4_1_2__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1_2__asympt_1,de_c1_4_1_2__asympt_1,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e7_4__asympt_1,e8_4__asympt_1,e1_4_1_2__asympt_1,t64_power,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.35),file(asympt_1,e2_4_1_2_1__asympt_1),[file(asympt_1,e2_4_1_2_1__asympt_1)]]).

fof(e5_4_1_2__asympt_1,plain,(
    k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_2__asympt_1) = k4_real_1(k6_power(c2_4__asympt_1,c1_4__asympt_1),k6_power(c1_4__asympt_1,c2_4_1_2__asympt_1)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1,dt_c2_4_1_2__asympt_1,dt_c1_4__asympt_1,dt_c2_4__asympt_1,e1_4_1_2__asympt_1])],[e1_4_1_2_1__asympt_1,e2_4_1_2_1__asympt_1]),
    [interesting(0.5),file(asympt_1,e5_4_1_2__asympt_1),[file(asympt_1,e5_4_1_2__asympt_1)]]).

fof(e2_4_1_2__asympt_1,plain,(
    ~ r1_xreal_0(k1_nat_1(c4_4_1__asympt_1,1),k1_nat_1(c4_4_1__asympt_1,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_int_1,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,rc5_asympt_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc6_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k2_xcmplx_0,dt_c4_4_1__asympt_1,cc2_xreal_0,fc3_xreal_0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t10_xreal_1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(asympt_1,e2_4_1_2__asympt_1),[file(asympt_1,e2_4_1_2__asympt_1)]]).

fof(e3_4_1_2__asympt_1,plain,(
    ~ r1_xreal_0(c2_4_1_2__asympt_1,c4_4_1__asympt_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1,e1_4_1_2__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc3_int_1,fc4_int_1,fc5_membered,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_int_1,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc2_membered,fc30_xreal_0,fc3_xreal_0,fc5_int_1,fc8_xreal_0,fc9_int_1,rc1_xreal_0,rc5_asympt_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealAdd__k2_xcmplx_0__rm1_r2_r1,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,dt_k1_nat_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_4_1_2__asympt_1,dt_c2_4_1_2__asympt_1,dt_c4_4_1__asympt_1,de_c1_4_1_2__asympt_1,cc2_xreal_0,fc1_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e2_4_1_2__asympt_1,e1_4_1_2__asympt_1,t2_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.5),file(asympt_1,e3_4_1_2__asympt_1),[file(asympt_1,e3_4_1_2__asympt_1)]]).

fof(e8_4_1__asympt_1,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c4_4_1__asympt_1,A)
       => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,A),k4_real_1(c3_4_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,A)))
          & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,A)) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_asympt_0,cc3_membered,fc4_subset_1,rc1_membered,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_xreal_0,cc2_asympt_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc5_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_subset_1,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c2_4_1__asympt_1,dt_c3_4_1__asympt_1,dt_c4_4_1__asympt_1,dt_c6_4__asympt_1,cc2_int_1,fc2_membered,spc0_numerals,spc0_boole,dh_c3_4_1__asympt_1,dh_c4_4_1__asympt_1,e6_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,e8_4_1__asympt_1),[file(asympt_1,e8_4_1__asympt_1)]]).

fof(e4_4_1_2__asympt_1,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1),k4_real_1(c3_4_1__asympt_1,k2_seq_1(k5_numbers,k1_numbers,c6_4__asympt_1,c2_4_1_2__asympt_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4_1_2__asympt_1,e1_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c4_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_asympt_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k5_numbers,dt_m2_subset_1,dt_c2_4_1__asympt_1,dt_c2_4_1_2__asympt_1,dt_c3_4_1__asympt_1,dt_c4_4_1__asympt_1,dt_c6_4__asympt_1,de_c6_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_4_1_2__asympt_1,e8_4_1__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(asympt_1,e4_4_1_2__asympt_1),[file(asympt_1,e4_4_1_2__asympt_1)]]).

fof(e6_4_1_2__asympt_1,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k6_power(c1_4__asympt_1,c2_4_1_2__asympt_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1,dt_c2_4_1_2__asympt_1,e1_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc3_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,dt_c4_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc4_xreal_0,fc5_int_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc2_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_power,dt_c1_4__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1__asympt_1,dt_c2_4_1_2__asympt_1,dt_c3_4_1__asympt_1,dt_c6_4__asympt_1,de_c6_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e5_4_1_2__asympt_1,e4_4_1_2__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.5),file(asympt_1,e6_4_1_2__asympt_1),[file(asympt_1,e6_4_1_2__asympt_1)]]).

fof(e7_4_1_2__asympt_1,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_2__asympt_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_4__asympt_1,e1_4__asympt_1,dt_c1_4__asympt_1,dt_c2_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1,e3_4__asympt_1,e1_4_1_2__asympt_1])],[commutativity_k2_xcmplx_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_int_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc3_int_1,fc3_xreal_0,fc4_int_1,fc4_subset_1,fc6_int_1,fc6_membered,fc7_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_xreal_0,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,spc1_arithm,spc5_arithm,spc6_arithm,spc8_arithm,t1_arithm,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k1_nat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_k1_nat_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_nat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c4_4_1__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc4_xreal_0,fc5_int_1,fc5_membered,fc5_xreal_0,fc9_int_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc2_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_power,dt_k6_xcmplx_0,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c1_4_1_2__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1__asympt_1,dt_c2_4_1_2__asympt_1,dt_c3_4__asympt_1,dt_c3_4_1__asympt_1,dt_c5_4__asympt_1,de_c1_4_1_2__asympt_1,de_c5_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e6_4_1_2__asympt_1,e3_4__asympt_1,e1_4_1_2__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.5),file(asympt_1,e7_4_1_2__asympt_1),[file(asympt_1,e7_4_1_2__asympt_1)]]).

fof(e8_4_1_2__asympt_1,plain,(
    r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1,e1_4_1_2__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,spc7_arithm,t1_subset,t2_arithm,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k3_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c4_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc2_subset_1,rqRealMult__k3_xcmplx_0__r0_r0_r0,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_m2_subset_1,dt_c2_4_1__asympt_1,dt_c2_4_1_2__asympt_1,dt_c3_4_1__asympt_1,dt_c4_4_1__asympt_1,dt_c6_4__asympt_1,de_c6_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e8_4_1__asympt_1,e3_4_1_2__asympt_1]),
    [interesting(0.5),file(asympt_1,e8_4_1_2__asympt_1),[file(asympt_1,e8_4_1_2__asympt_1)]]).

fof(i5_4_1_2__asympt_1,theorem,(
    $true ),
    introduced(tautology,[file(asympt_1,i5_4_1_2__asympt_1)]),
    [interesting(0.5),trivial,file(asympt_1,i5_4_1_2__asympt_1)]).

fof(i4_4_1_2__asympt_1,plain,(
    r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1,e1_4_1_2__asympt_1])],[e8_4_1_2__asympt_1,i5_4_1_2__asympt_1]),
    [interesting(0.5),file(asympt_1,i4_4_1_2__asympt_1),[file(asympt_1,i4_4_1_2__asympt_1)]]).

fof(i3_4_1_2__asympt_1,plain,
    ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_2__asympt_1)))
    & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_4__asympt_1,e1_4__asympt_1,dt_c1_4__asympt_1,e3_4__asympt_1,dt_c2_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1,e1_4_1_2__asympt_1])],[e7_4_1_2__asympt_1,i4_4_1_2__asympt_1]),
    [interesting(0.5),file(asympt_1,i3_4_1_2__asympt_1),[file(asympt_1,i3_4_1_2__asympt_1)]]).

fof(i2_4_1_2__asympt_1,plain,
    ( r1_xreal_0(c1_4_1_2__asympt_1,c2_4_1_2__asympt_1)
   => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_2__asympt_1)))
      & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__asympt_1,e1_4__asympt_1,dt_c1_4__asympt_1,e3_4__asympt_1,dt_c2_4_1_2__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1]),discharge_asm(discharge,[e1_4_1_2__asympt_1])],[e1_4_1_2__asympt_1,i3_4_1_2__asympt_1]),
    [interesting(0.5),file(asympt_1,i2_4_1_2__asympt_1),[file(asympt_1,i2_4_1_2__asympt_1)]]).

fof(i2_4_1_2_tmp__asympt_1,plain,
    ( m2_subset_1(c2_4_1_2__asympt_1,k1_numbers,k5_numbers)
   => ( r1_xreal_0(c1_4_1_2__asympt_1,c2_4_1_2__asympt_1)
     => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,c2_4_1_2__asympt_1)))
        & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,c2_4_1_2__asympt_1)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__asympt_1,e1_4__asympt_1,dt_c1_4__asympt_1,e3_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1]),discharge_asm(discharge,[dt_c2_4_1_2__asympt_1])],[dt_c2_4_1_2__asympt_1,i2_4_1_2__asympt_1]),
    [interesting(0.5),i1_4_1_2__asympt_1]).

fof(i1_4_1_2__asympt_1,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c1_4_1_2__asympt_1,A)
       => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,A),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,A)))
          & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,A)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_4__asympt_1,e1_4__asympt_1,dt_c1_4__asympt_1,e3_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[i2_4_1_2_tmp__asympt_1,dh_c2_4_1_2__asympt_1]),
    [interesting(0.5),file(asympt_1,i1_4_1_2__asympt_1),[file(asympt_1,i1_4_1_2__asympt_1)]]).

fof(e12_4_1__asympt_1,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => ( r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,B),k4_real_1(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k2_seq_1(k5_numbers,k1_numbers,c5_4__asympt_1,B)))
              & r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,c2_4_1__asympt_1,B)) ) ) ) ) ),
    inference(take,[status(thm),assumptions([dt_c3_4__asympt_1,e1_4__asympt_1,dt_c1_4__asympt_1,e3_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dt_k1_funct_2,dt_k2_zfmisc_1,dt_m1_fraenkel,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_asympt_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,rc5_asympt_0,rc6_asympt_0,commutativity_k3_xcmplx_0,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_k5_power,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc2_subset_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_real_1,dt_k5_numbers,dt_k6_power,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c1_4_1_2__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1__asympt_1,dt_c3_4_1__asympt_1,dt_c5_4__asympt_1,fc2_membered,spc0_numerals,spc0_boole,i1_4_1_2__asympt_1]),
    [interesting(0.65),file(asympt_1,e12_4_1__asympt_1),[file(asympt_1,e12_4_1__asympt_1)]]).

fof(e4_4_1__asympt_1,plain,(
    c1_4_1__asympt_1 = c2_4_1__asympt_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dh_c2_4_1__asympt_1,e3_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,e4_4_1__asympt_1),[file(asympt_1,e4_4_1__asympt_1)]]).

fof(e9_4_1__asympt_1,plain,(
    ~ r1_xreal_0(k6_power(c2_4__asympt_1,c1_4__asympt_1),k6_power(c2_4__asympt_1,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1,dt_c2_4__asympt_1,e1_4__asympt_1,e2_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k6_power,dt_k5_power,dt_k6_power,dt_c1_4__asympt_1,dt_c2_4__asympt_1,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_4__asympt_1,e2_4__asympt_1,t65_power,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.65),file(asympt_1,e9_4_1__asympt_1),[file(asympt_1,e9_4_1__asympt_1)]]).

fof(e10_4_1__asympt_1,plain,(
    ~ r1_xreal_0(k6_power(c2_4__asympt_1,c1_4__asympt_1),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1,e1_4__asympt_1,e2_4__asympt_1,dt_c2_4__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k6_power,dt_k5_power,dt_k6_power,dt_c1_4__asympt_1,dt_c2_4__asympt_1,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e9_4_1__asympt_1,e8_4__asympt_1,t59_power,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.65),file(asympt_1,e10_4_1__asympt_1),[file(asympt_1,e10_4_1__asympt_1)]]).

fof(e7_4_1__asympt_1,plain,(
    ~ r1_xreal_0(c3_4_1__asympt_1,0) ),
    inference(consider,[status(thm),assumptions([dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[dh_c3_4_1__asympt_1,dh_c4_4_1__asympt_1,e6_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,e7_4_1__asympt_1),[file(asympt_1,e7_4_1__asympt_1)]]).

fof(e11_4_1__asympt_1,plain,(
    ~ r1_xreal_0(k4_real_1(c3_4_1__asympt_1,k6_power(c2_4__asympt_1,c1_4__asympt_1)),k4_real_1(c3_4_1__asympt_1,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__asympt_1,e1_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc5_membered,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc1_subset_1,rc2_asympt_0,rc2_int_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_power,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_real_1,redefinition_k6_power,dt_k3_xcmplx_0,dt_k4_real_1,dt_k6_power,dt_c1_4__asympt_1,dt_c2_4__asympt_1,dt_c3_4_1__asympt_1,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e10_4_1__asympt_1,e7_4_1__asympt_1,t70_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.65),file(asympt_1,e11_4_1__asympt_1),[file(asympt_1,e11_4_1__asympt_1)]]).

fof(e13_4_1__asympt_1,plain,(
    r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[reflexivity_r1_tarski,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc4_subset_1,fc6_membered,fc7_int_1,rc1_asympt_0,rc1_int_1,rc1_membered,rc2_asympt_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_asympt_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_power,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_c3_4__asympt_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_asympt_0,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_asympt_0,rc5_asympt_0,rc6_asympt_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_0_asympt_0,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k6_power,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k5_asympt_0,dt_k5_numbers,dt_k6_power,dt_m2_subset_1,dt_c1_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c2_4_1__asympt_1,dt_c3_4_1__asympt_1,dt_c5_4__asympt_1,de_c5_4__asympt_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,t1_subset,t7_boole,d12_asympt_0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e12_4_1__asympt_1,e4_4_1__asympt_1,e11_4_1__asympt_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.65),file(asympt_1,e13_4_1__asympt_1),[file(asympt_1,e13_4_1__asympt_1)]]).

fof(i4_4_1__asympt_1,theorem,(
    $true ),
    introduced(tautology,[file(asympt_1,i4_4_1__asympt_1)]),
    [interesting(0.65),trivial,file(asympt_1,i4_4_1__asympt_1)]).

fof(i3_4_1__asympt_1,plain,(
    r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1,e2_4_1__asympt_1])],[e13_4_1__asympt_1,i4_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,i3_4_1__asympt_1),[file(asympt_1,i3_4_1__asympt_1)]]).

fof(i2_4_1__asympt_1,plain,
    ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1))
   => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1]),discharge_asm(discharge,[e2_4_1__asympt_1])],[e2_4_1__asympt_1,i3_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,i2_4_1__asympt_1),[file(asympt_1,i2_4_1__asympt_1)]]).

fof(i1_4_1__asympt_1,plain,
    ( ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1))
     => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1)) )
    & ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1))
     => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1)) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c1_4_1__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[e1_4_1__asympt_1,i2_4_1__asympt_1]),
    [interesting(0.65),file(asympt_1,i1_4_1__asympt_1),[file(asympt_1,i1_4_1__asympt_1)]]).

fof(i1_4_1_tmp__asympt_1,plain,
    ( ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1))
     => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1)) )
    & ( r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c6_4__asympt_1))
     => r2_hidden(c1_4_1__asympt_1,k5_asympt_0(c5_4__asympt_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1]),discharge_asm(discharge,[dt_c1_4_1__asympt_1])],[dt_c1_4_1__asympt_1,i1_4_1__asympt_1]),
    [interesting(0.8),e9_4__asympt_1]).

fof(e9_4__asympt_1,plain,(
    ! [A] : 
      ( ( r2_hidden(A,k5_asympt_0(c5_4__asympt_1))
       => r2_hidden(A,k5_asympt_0(c6_4__asympt_1)) )
      & ( r2_hidden(A,k5_asympt_0(c6_4__asympt_1))
       => r2_hidden(A,k5_asympt_0(c5_4__asympt_1)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[i1_4_1_tmp__asympt_1,dh_c1_4_1__asympt_1]),
    [interesting(0.8),file(asympt_1,e9_4__asympt_1),[file(asympt_1,e9_4__asympt_1)]]).

fof(e10_4__asympt_1,plain,
    ( c5_4__asympt_1 = c3_4__asympt_1
    & c6_4__asympt_1 = c4_4__asympt_1
    & k5_asympt_0(c5_4__asympt_1) = k5_asympt_0(c6_4__asympt_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[commutativity_k3_xcmplx_0,reflexivity_r1_tarski,dt_k1_funct_1,dt_k1_funct_2,dt_k3_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc4_xreal_0,fc7_int_1,rc1_asympt_0,rc2_asympt_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_asympt_0,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc7_arithm,t1_real,t2_arithm,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_fraenkel,existence_m2_subset_1,redefinition_k1_fraenkel,redefinition_k2_seq_1,redefinition_k4_real_1,redefinition_m2_fraenkel,redefinition_m2_subset_1,dt_k1_fraenkel,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_seq_1,dt_k2_zfmisc_1,dt_k4_real_1,dt_k5_ordinal2,dt_m2_fraenkel,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,fc6_membered,rc1_int_1,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_int_1,rc2_subset_1,rc4_asympt_0,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_boole,t1_numerals,t2_real,t3_real,t3_subset,t4_subset,t5_subset,spc0_numerals,spc0_boole,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc2_asympt_0,cc2_int_1,fc2_membered,t2_subset,t6_boole,t8_boole,fraenkel_a_1_0_asympt_0,antisymmetry_r2_hidden,dt_k5_asympt_0,dt_c3_4__asympt_1,dt_c4_4__asympt_1,dt_c5_4__asympt_1,dt_c6_4__asympt_1,de_c5_4__asympt_1,de_c6_4__asympt_1,t1_subset,t7_boole,d12_asympt_0,e9_4__asympt_1,t2_tarski]),
    [interesting(0.8),file(asympt_1,e10_4__asympt_1),[file(asympt_1,e10_4__asympt_1)]]).

fof(i6_4__asympt_1,theorem,(
    $true ),
    introduced(tautology,[file(asympt_1,i6_4__asympt_1)]),
    [interesting(0.8),trivial,file(asympt_1,i6_4__asympt_1)]).

fof(i5_4__asympt_1,plain,
    ( c5_4__asympt_1 = c3_4__asympt_1
    & c6_4__asympt_1 = c4_4__asympt_1
    & k5_asympt_0(c5_4__asympt_1) = k5_asympt_0(c6_4__asympt_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[e10_4__asympt_1,i6_4__asympt_1]),
    [interesting(0.8),file(asympt_1,i5_4__asympt_1),[file(asympt_1,i5_4__asympt_1)]]).

fof(i4_4__asympt_1,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v4_asympt_0(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & c5_4__asympt_1 = c3_4__asympt_1
      & A = c4_4__asympt_1
      & k5_asympt_0(c5_4__asympt_1) = k5_asympt_0(A) ) ),
    inference(take,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_asympt_0,rc2_asympt_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_asympt_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_int_1,rc4_asympt_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc2_asympt_0,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_asympt_0,dt_k5_numbers,dt_m2_relset_1,dt_c3_4__asympt_1,dt_c4_4__asympt_1,dt_c5_4__asympt_1,dt_c6_4__asympt_1,fc2_membered,i5_4__asympt_1]),
    [interesting(0.8),file(asympt_1,i4_4__asympt_1),[file(asympt_1,i4_4__asympt_1)]]).

fof(i3_4__asympt_1,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v4_asympt_0(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & ? [B] : 
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & v4_asympt_0(B)
          & m2_relset_1(B,k5_numbers,k1_numbers)
          & A = c3_4__asympt_1
          & B = c4_4__asympt_1
          & k5_asympt_0(A) = k5_asympt_0(B) ) ) ),
    inference(take,[status(thm),assumptions([dt_c3_4__asympt_1,e3_4__asympt_1,dt_c1_4__asympt_1,e1_4__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1,e2_4__asympt_1,e4_4__asympt_1])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_asympt_0,rc2_asympt_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_asympt_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_asympt_0,cc3_int_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_int_1,rc4_asympt_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc2_asympt_0,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_asympt_0,dt_k5_numbers,dt_m2_relset_1,dt_c3_4__asympt_1,dt_c4_4__asympt_1,dt_c5_4__asympt_1,fc2_membered,i4_4__asympt_1]),
    [interesting(0.8),file(asympt_1,i3_4__asympt_1),[file(asympt_1,i3_4__asympt_1)]]).

fof(i2_4__asympt_1,plain,(
    ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
      & ~ r1_xreal_0(c2_4__asympt_1,1)
      & k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,0) = 0
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(A,0)
           => k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,A) = k6_power(c1_4__asympt_1,A) ) )
      & k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,0) = 0
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(A,0)
           => k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,A) = k6_power(c2_4__asympt_1,A) ) )
      & ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,k5_numbers,k1_numbers)
            & v4_asympt_0(A)
            & m2_relset_1(A,k5_numbers,k1_numbers) )
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( A = c3_4__asympt_1
                  & B = c4_4__asympt_1
                  & k5_asympt_0(A) = k5_asympt_0(B) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__asympt_1,dt_c1_4__asympt_1,dt_c2_4__asympt_1,dt_c4_4__asympt_1]),discharge_asm(discharge,[e1_4__asympt_1,e2_4__asympt_1,e3_4__asympt_1,e4_4__asympt_1])],[e1_4__asympt_1,e2_4__asympt_1,e3_4__asympt_1,e4_4__asympt_1,i3_4__asympt_1]),
    [interesting(0.8),file(asympt_1,i2_4__asympt_1),[file(asympt_1,i2_4__asympt_1)]]).

fof(i2_4_tmp__asympt_1,plain,
    ( ( v1_funct_1(c3_4__asympt_1)
      & v1_funct_2(c3_4__asympt_1,k5_numbers,k1_numbers)
      & m2_relset_1(c3_4__asympt_1,k5_numbers,k1_numbers)
      & v1_funct_1(c4_4__asympt_1)
      & v1_funct_2(c4_4__asympt_1,k5_numbers,k1_numbers)
      & m2_relset_1(c4_4__asympt_1,k5_numbers,k1_numbers) )
   => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
        & ~ r1_xreal_0(c2_4__asympt_1,1)
        & k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,0) = 0
        & ! [A] : 
            ( m2_subset_1(A,k1_numbers,k5_numbers)
           => ( ~ r1_xreal_0(A,0)
             => k2_seq_1(k5_numbers,k1_numbers,c3_4__asympt_1,A) = k6_power(c1_4__asympt_1,A) ) )
        & k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,0) = 0
        & ! [A] : 
            ( m2_subset_1(A,k1_numbers,k5_numbers)
           => ( ~ r1_xreal_0(A,0)
             => k2_seq_1(k5_numbers,k1_numbers,c4_4__asympt_1,A) = k6_power(c2_4__asympt_1,A) ) )
        & ! [A] : 
            ( ( v1_funct_1(A)
              & v1_funct_2(A,k5_numbers,k1_numbers)
              & v4_asympt_0(A)
              & m2_relset_1(A,k5_numbers,k1_numbers) )
           => ! [B] : 
                ( ( v1_funct_1(B)
                  & v1_funct_2(B,k5_numbers,k1_numbers)
                  & v4_asympt_0(B)
                  & m2_relset_1(B,k5_numbers,k1_numbers) )
               => ~ ( A = c3_4__asympt_1
                    & B = c4_4__asympt_1
                    & k5_asympt_0(A) = k5_asympt_0(B) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__asympt_1,dt_c2_4__asympt_1]),discharge_asm(discharge,[dt_c3_4__asympt_1,dt_c4_4__asympt_1])],[dt_c3_4__asympt_1,dt_c4_4__asympt_1,i2_4__asympt_1]),
    [interesting(0.8),i1_4__asympt_1]).

fof(i1_4__asympt_1,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
              & ~ r1_xreal_0(c2_4__asympt_1,1)
              & k2_seq_1(k5_numbers,k1_numbers,A,0) = 0
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,0)
                   => k2_seq_1(k5_numbers,k1_numbers,A,C) = k6_power(c1_4__asympt_1,C) ) )
              & k2_seq_1(k5_numbers,k1_numbers,B,0) = 0
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k6_power(c2_4__asympt_1,C) ) )
              & ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v4_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k5_numbers,k1_numbers)
                        & v4_asympt_0(D)
                        & m2_relset_1(D,k5_numbers,k1_numbers) )
                     => ~ ( C = A
                          & D = B
                          & k5_asympt_0(C) = k5_asympt_0(D) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__asympt_1,dt_c2_4__asympt_1])],[i2_4_tmp__asympt_1,dh_c3_4__asympt_1,dh_c4_4__asympt_1]),
    [interesting(0.8),file(asympt_1,i1_4__asympt_1),[file(asympt_1,i1_4__asympt_1)]]).

fof(i1_4_tmp__asympt_1,plain,
    ( ( v1_asympt_0(c1_4__asympt_1)
      & m1_subset_1(c1_4__asympt_1,k1_numbers)
      & v1_asympt_0(c2_4__asympt_1)
      & m1_subset_1(c2_4__asympt_1,k1_numbers) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & m2_relset_1(A,k5_numbers,k1_numbers) )
       => ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,k1_numbers)
              & m2_relset_1(B,k5_numbers,k1_numbers) )
           => ~ ( ~ r1_xreal_0(c1_4__asympt_1,1)
                & ~ r1_xreal_0(c2_4__asympt_1,1)
                & k2_seq_1(k5_numbers,k1_numbers,A,0) = 0
                & ! [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(C,0)
                     => k2_seq_1(k5_numbers,k1_numbers,A,C) = k6_power(c1_4__asympt_1,C) ) )
                & k2_seq_1(k5_numbers,k1_numbers,B,0) = 0
                & ! [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(C,0)
                     => k2_seq_1(k5_numbers,k1_numbers,B,C) = k6_power(c2_4__asympt_1,C) ) )
                & ! [C] : 
                    ( ( v1_funct_1(C)
                      & v1_funct_2(C,k5_numbers,k1_numbers)
                      & v4_asympt_0(C)
                      & m2_relset_1(C,k5_numbers,k1_numbers) )
                   => ! [D] : 
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,k5_numbers,k1_numbers)
                          & v4_asympt_0(D)
                          & m2_relset_1(D,k5_numbers,k1_numbers) )
                       => ~ ( C = A
                            & D = B
                            & k5_asympt_0(C) = k5_asympt_0(D) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__asympt_1,dt_c2_4__asympt_1])],[dt_c1_4__asympt_1,dt_c2_4__asympt_1,i1_4__asympt_1]),
    [interesting(1),t2_asympt_1]).

fof(t2_asympt_1,theorem,(
    ! [A] : 
      ( ( v1_asympt_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] : 
          ( ( v1_asympt_0(B)
            & m1_subset_1(B,k1_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_numbers)
                    & m2_relset_1(D,k5_numbers,k1_numbers) )
                 => ~ ( ~ r1_xreal_0(A,1)
                      & ~ r1_xreal_0(B,1)
                      & k2_seq_1(k5_numbers,k1_numbers,C,0) = 0
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(E,0)
                           => k2_seq_1(k5_numbers,k1_numbers,C,E) = k6_power(A,E) ) )
                      & k2_seq_1(k5_numbers,k1_numbers,D,0) = 0
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(E,0)
                           => k2_seq_1(k5_numbers,k1_numbers,D,E) = k6_power(B,E) ) )
                      & ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_numbers,k1_numbers)
                            & v4_asympt_0(E)
                            & m2_relset_1(E,k5_numbers,k1_numbers) )
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,k5_numbers,k1_numbers)
                                & v4_asympt_0(F)
                                & m2_relset_1(F,k5_numbers,k1_numbers) )
                             => ~ ( E = C
                                  & F = D
                                  & k5_asympt_0(E) = k5_asympt_0(F) ) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__asympt_1,dh_c1_4__asympt_1,dh_c2_4__asympt_1]),
    [interesting(1),file(asympt_1,t2_asympt_1),[file(asympt_1,t2_asympt_1)]]).